Question

Thực hiện phép tính:

\(\dfrac{3}{x+5}-\dfrac{2}{x+2}\)

Answer 1

Ta có: \(\dfrac{3}{x+5}=\dfrac{3.\left(x+2\right)}{\left(x+5\right).\left(x+2\right)}=\dfrac{3x+6}{x^2+5x+2x+10}=\dfrac{3x+6}{x^2+7x+10}\)

\(\dfrac{2}{x+2}=\dfrac{2.\left(x+5\right)}{\left(x+2\right).\left(x+5\right)}=\dfrac{2x+10}{x^2+5x+2x+10}=\dfrac{2x+10}{x^2+7x+10}\)

\(\Rightarrow\dfrac{3}{x+5}-\dfrac{2}{x+2}=\dfrac{3x+6}{x^2+7x+10}-\dfrac{2x+10}{x^2+7x+10}=\dfrac{3x+6-2x-10}{x^2+7x+10}=\dfrac{x-4}{x^2+7x+10}\)